On Sat, Oct 8, 2011 at 11:27 PM, Dale Tronrud <det102 at uoxray.uoregon.edu> wrote:
> "more precise than is actually the case"? I don't understand this.
> A map has precision to infinitely fine spacing. The sampling grids we
> choose are the artifacts - the courser the grid the worst the
> representation.
> The prismatic points and spikes of a coarsely sampled map are aliasing
> artifacts. A smoothly varying surface is an accurate representation of
> the continuous density function.
The spacing between grid points is telling you something about how
well each of those grid points is resolved. Even if the electron
density is continuous, it still comes from an incomplete Fourier
series and is full of artifacts and ambiguity. Spacing your grid
points every d_min/6 A implies (to my eyes, anyway) that the optical
resolution allows you to accurately distinguish the values at those
points, which isn't actually the case. It's not necessarily
mathematically inaccurate, but since most of us are trained to
model-build using a grid spacing of d_min/3 or d_min/4 (or whatever
the default is in Coot), we "know" what a 3A map looks like, and a
1.5A map, etc.
(I know this is all nit-picking, but I have in mind a specific figure
in a methods paper where the authors compared a 2mFo-DFc map before
and after their magical map improvement procedure, with much more
detail visible in the "after" maps. I had to read it twice to realize
that the "after" map had a much finer grid spacing - of course it
looked much better!)
-Nat